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Math Problems
Calculus
Average rate of change I
We want to solve the following equation.
x
3
=
∣
x
−
2
∣
−
1
\sqrt[3]{x}=|x-2|-1
3
x
=
∣
x
−
2∣
−
1
One of the solutions is
x
≈
0.3
x\approx 0.3
x
≈
0.3
. Find the other solution. Hint: Use a graphing calculator. Round your answer to the nearest tenth.
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We want to solve the following equation.
x
3
=
∣
x
−
2
∣
−
1
\sqrt[3]{x}=|x-2|-1
3
x
=
∣
x
−
2∣
−
1
One of the solutions is
x
≈
0.3
x\approx 0.3
x
≈
0.3
. Find the other solution. Hint: Use a graphing calculator. Round your answer to the nearest tenth.
Get tutor help
t
t
t
g
(
t
)
g(t)
g
(
t
)
−
5
-5
−
5
6
6
6
−
4
-4
−
4
4
4
4
−
3
-3
−
3
2
2
2
−
2
-2
−
2
1
1
1
g
(
t
)
g(t)
g
(
t
)
0
0
0
g
(
t
)
g(t)
g
(
t
)
0
0
0
g
(
t
)
g(t)
g
(
t
)
2
2
2
−
2
-2
−
2
1
1
1
−
3
-3
−
3
2
2
2
1
1
1
g
(
t
)
g(t)
g
(
t
)
8
8
8
g
(
t
)
g(t)
g
(
t
)
8
8
8
4
4
4
6
6
6
−
5
-5
−
5
2
2
2
−
5
-5
−
5
3
3
3
What is the average rate of change of
−
5
-5
−
5
4
4
4
over the interval
−
5
-5
−
5
5
5
5
? Give an exact number.
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quizizz.com/join/game/U
2
2
2
FsdGVkX
18
18
18
ZGorQoo
1
1
1
IBNwuuEvbQo\%
252
252
252
B
0
0
0
wmVInYz
7
7
7
SGug
9
9
9
q|Y\%
252
252
252
BRZ
8
8
8
LpkdAUrvsRTd
40
40
40
pcTO
8
8
8
\%
252
252
252
FrY
88
88
88
Z
1
1
1
i
3
3
3
\%
252
252
252
FIp
2
2
2
Ig\%
253
253
253
D\%
253
253
253
D?ga...
\newline
18
/
90
18 / 90
18/90
\newline
Kelly made fruit punch to serve at a party for her chess team. She mixed
12
/
5
12 / 5
12/5
liters of cranberry juice and
13
/
5
13 / 5
13/5
liters of pineapple juice together. Then, she split the fruit punch evenly among
9
9
9
glasses. How much fruit punch did Kelly pour into each glass?
\newline
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
\newline
|Type your answer...
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Simplify to create an equivalent expression.
\newline
−
3
z
−
(
−
z
−
2
)
-3z-(-z-2)
−
3
z
−
(
−
z
−
2
)
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
−
4
-4
−
4
z+
2
2
2
\newline
(B)
\newline
−
2
-2
−
2
z
−
2
-2
−
2
\newline
(C)
\newline
−
2
-2
−
2
z+
2
2
2
\newline
(D)
\newline
4
4
4
z+
2
2
2
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Find the average rate of change of
f
(
x
)
=
−
x
+
17
f(x) = -x + 17
f
(
x
)
=
−
x
+
17
between
x
=
2
x = 2
x
=
2
and
x
=
2
+
h
x = 2 + h
x
=
2
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
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Find the average rate of change of
g
(
x
)
=
x
+
15
g(x) = x + 15
g
(
x
)
=
x
+
15
between
x
=
−
5
x = -5
x
=
−
5
and
x
=
−
5
+
h
x = -5 + h
x
=
−
5
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
f
(
x
)
=
−
2
x
f(x) = -2x
f
(
x
)
=
−
2
x
between
x
=
−
3
x = -3
x
=
−
3
and
x
=
−
3
+
h
x = -3 + h
x
=
−
3
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
f
(
x
)
=
x
−
4
f(x) = x - 4
f
(
x
)
=
x
−
4
between
x
=
5
x = 5
x
=
5
and
x
=
5
+
h
x = 5 + h
x
=
5
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
g
(
x
)
=
x
+
11
g(x) = x + 11
g
(
x
)
=
x
+
11
between
x
=
4
x = 4
x
=
4
and
x
=
4
+
h
x = 4 + h
x
=
4
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
f
(
x
)
=
−
x
+
6
f(x) = -x + 6
f
(
x
)
=
−
x
+
6
between
x
=
4
x = 4
x
=
4
and
x
=
4
+
h
x = 4 + h
x
=
4
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
g
(
x
)
=
x
+
14
g(x) = x + 14
g
(
x
)
=
x
+
14
between
x
=
5
x = 5
x
=
5
and
x
=
5
+
h
x = 5 + h
x
=
5
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
g
(
x
)
=
−
8
−
x
g(x) = -8 - x
g
(
x
)
=
−
8
−
x
between
x
=
4
x = 4
x
=
4
and
x
=
4
+
h
x = 4 + h
x
=
4
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
g
(
x
)
=
−
3
x
+
8
g(x) = -3x + 8
g
(
x
)
=
−
3
x
+
8
between
x
=
2
x = 2
x
=
2
and
x
=
2
+
h
x = 2 + h
x
=
2
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
f
(
x
)
=
−
10
x
2
f(x) = -10x^2
f
(
x
)
=
−
10
x
2
between
x
=
0
x = 0
x
=
0
and
x
=
h
x = h
x
=
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
f
(
x
)
=
8
x
2
−
19
f(x) = 8x^2 - 19
f
(
x
)
=
8
x
2
−
19
between
x
=
0
x = 0
x
=
0
and
x
=
h
x = h
x
=
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
g
(
x
)
=
9
x
2
+
14
g(x) = 9x^2 + 14
g
(
x
)
=
9
x
2
+
14
between
x
=
0
x = 0
x
=
0
and
x
=
h
x = h
x
=
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
f
(
x
)
=
−
x
f(x) = -x
f
(
x
)
=
−
x
between
x
=
6
x = 6
x
=
6
and
x
=
6
+
h
x = 6 + h
x
=
6
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
k
(
x
)
=
3
x
k(x) = 3x
k
(
x
)
=
3
x
between
x
=
−
4
x = -4
x
=
−
4
and
x
=
−
4
+
h
x = -4 + h
x
=
−
4
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
f
(
x
)
=
x
+
16
f(x) = x + 16
f
(
x
)
=
x
+
16
between
x
=
−
2
x = -2
x
=
−
2
and
x
=
−
2
+
h
x = -2 + h
x
=
−
2
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
k
(
x
)
=
10
x
2
−
11
k(x) = 10x^2 - 11
k
(
x
)
=
10
x
2
−
11
between
x
=
0
x = 0
x
=
0
and
x
=
h
x = h
x
=
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
g
(
x
)
=
20
g(x) = 20
g
(
x
)
=
20
between
x
=
−
3
x = -3
x
=
−
3
and
x
=
−
3
+
h
x = -3 + h
x
=
−
3
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
k
(
x
)
=
x
−
16
k(x) = x - 16
k
(
x
)
=
x
−
16
between
x
=
−
4
x = -4
x
=
−
4
and
x
=
−
4
+
h
x = -4 + h
x
=
−
4
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
k
(
x
)
=
x
k(x) = x
k
(
x
)
=
x
between
x
=
4
x = 4
x
=
4
and
x
=
4
+
h
x = 4 + h
x
=
4
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Find the average rate of change of
k
(
x
)
=
x
−
8
k(x) = x - 8
k
(
x
)
=
x
−
8
between
x
=
−
7
x = -7
x
=
−
7
and
x
=
−
7
+
h
x = -7 + h
x
=
−
7
+
h
, where
h
≠
0
h \neq 0
h
=
0
.
\newline
Simplify your answer. Your answer may be a number or an expression in terms of
h
h
h
.
Get tutor help
Solve for
r
r
r
.
\newline
−
1.3
r
−
15
+
12.2
r
>
17.16
+
17.6
r
-1.3r - 15 + 12.2r > 17.16 + 17.6r
−
1.3
r
−
15
+
12.2
r
>
17.16
+
17.6
r
\newline
Write your answer using a decimal, whole number, or fraction in lowest terms.
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5
5
5
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\newline
Module Knowledge Check
\newline
Question
20
20
20
\newline
A farmer owns a total of
10
10
10
acres of land. The land is separated into
4
2
3
4 \frac{2}{3}
4
3
2
equally sized sections. How many acres are in each section?
\newline
Write your answer as a mixed number in simplest form.
\newline
acres
\newline
Don't Know
\newline
Submit
\newline
Search.
\newline
2024
2024
2024
McGraw Hill UC. All Rights Rese
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